A woman in her 70s has become the first person to die with COVID-19 in the Territory, the Chief Minister Michael Gunner has said, while two people who travelled from interstate have also tested positive and have been put into quarantine in Howard Springs.

Chief Minister Michael Gunner told a press conference on Thursday morning the unvaccinated woman from the Binjari community died about 11.30pm on Thursday in Royal Darwin Hospital.

He said she was taken to the hospital from the community on November 20, had spent a substantiation amount of time receiving oxygen, and had other underlying health issues.

Mr Gunner said a man who had travelled from Melbourne with three family members on November 29 had tested positive to COVID-19 in home quarantine. The man was notified by Victorian authorities he had been at an exposure site and then tested positive, and was moved with his family to Howard Springs Mr Gunner said.

He said the second positive case was a woman who arrived with her two children from Adelaide on the Jetstar flight JQ-692 yesterday. Mr Gunner said she had taken a PCR test before she left, and while in the air the test came back positive, and she was taken to the Howard Springs camp.

He said there would be close contacts from the flight and South Australia would be declared a red zone from 8pm tonight.

Heath Minister Natasha Fyles told a press conference on Thursday a 45-year-old man from Lajamanu, about 560 kilometres south-west of Katherine, tested positive to COVID-19, becoming the first case from the Katherine Robinson River cluster which now stands at 60.

Mr Gunner said NT Health believed the man caught the virus on November 15 when he went to the Wurli-Wurlinjang health clinic in Katherine to receive his second COVID-19 vaccination.